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L. A. Markovich

Publications and source records attributed to L. A. Markovich.

22 records · Page 2Linked to original sources
arXiv2014

Separability and entanglement of spin $1$ particle

We define the separability and entanglement notion for particle with spin $s=1$. We consider two cases. In the first the particle is composed of two fermions with $s_1=1/2$ and $s_2=1/2$. In the second case the state is the qutrit state which is not composed system. The notion of negativity and concurrence is defined for the qutrit state. The concurrence and negativity of entangled and separable qutrit states determined by the parameters of the density matrix are explicitly calculated. The maximum entanglement of the qutrit state is observed for maximum values of non diagonal matrix elements of the density matrix. New entropic inequalities for the density matrix of the qutrit state are obtained.

quant-ph↗
arXiv2014

The equation of optimal filtering, Kalman's filter and Theorem on normal correlation

An important objective of the classical processing of stationary random sequences under nonparametric uncertainty is the problem of filtering in case when the distribution of the underlying signal is unknown. In this paper it is assumed that an unknown useful signal $(S_n)_{n\ge1}$ is Markov. This allows us to construct an estimate of the useful signal, expressed in terms of the distribution density function of an observable random sequence $(X_n)_{n\ge1}$. The equation of the optimal Bayesian estimation (so called equation of optimal filtering) of such signal has been received by A.V. Dobrovidov. Our main result is the following. It is proved that when the unobservable Markov sequence is defined by a linear equation with the Gaussian noise, the equation of optimal filtering coincides with the classical Kalman's filter and the conditional expectation defined by the theorem on normal correlation.

math.PR↗
arXiv2014

Separability and entanglement of the qudit X-state with j = 3/2

The qudit state for j = 3=2 with density matrix of the form corresponding to X-state of two-qubits is studied from the point of view of entanglement and separability properties. The method of qubit portrait of qudit states is used to get the entropic inequalities for the entangled state of the single qudit. The tomographic probability representation of the qudit X-state under consideration and its Shannon and q-entropic characteristics are presented in explicit form.

quant-ph↗